Question

Find p(t, the x component of the total momentum of the system at time t. express your answer in terms of m1, m2, v1(t, and v2(t.

Answer 1

The X-component of the momentum of the system is $\boxed{{p_x}={m_1}{v_1}\left(t\right)+{m_2}{v_2}\left(t\right)}$ .

Further Explanation:

The momentum of a body is the amount of motion contained by the body. The momentum of a body is expressed as the product of the mass and velocity of the body at the particular instant.

The momentum of the body is represented as:

$\boxed{p=m\times v}$

For a system of particles, the momentum of the whole system is the vector sum of individual momentum of all the particles.

${\vec p_{net}}={\vec p_1}+{\vec p_2}+{\vec p_3}.....$

Here, ${\vec p_{net}}$  is the net momentum of the system.

In the given question, both the particles are moving in the same direction i.e. X-direction. Therefore, the net momentum of the system in X-direction is the sum of the two momentum.

The velocity of the first particle at time $t$  is ${v_1}\left(t\right)$ .

The momentum of the first particle is:

${p_1}={m_1}{v_1}\left(t\right)$

The velocity of the second particle at time $t$  is ${v_2}\left(t\right)$ .

The momentum of the second particle is:

${p_2}={m_2}{v_2}\left(t\right)$

The X-component of the net momentum of the system is:

$\begin{aligned}{p_x}&={p_1}+{p_2}\\&={m_1}{v_1}\left(t\right)+{m_2}{v_2}\left(t\right)\\\end{aligned}$

Thus, the X-component of the momentum of the system is $\boxed{{p_x}={m_1}{v_1}\left(t\right)+{m_2}{v_2}\left(t\right)}$ .

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Answer Details:

Grade: High School

Subject: Physics

Chapter: Force and Momentum

Keywords:

Momentum, X-component, total momentum, isolated system, velocity of the particle, v1(t), v2(t), composed of two blocks, masses m1 and m2.